Browsing by Author "Mueller, Jennifer, committee member"
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Item Open Access Compound-Gaussian-regularized inverse problems: theory, algorithms, and neural networks(Colorado State University. Libraries, 2024) Lyons, Carter, author; Cheney, Margaret, advisor; Raj, Raghu G., advisor; Azimi, Mahmood, committee member; King, Emily, committee member; Mueller, Jennifer, committee memberLinear inverse problems are frequently encountered in a variety of applications including compressive sensing, radar, sonar, medical, and tomographic imaging. Model-based and data-driven methods are two prevalent classes of approaches used to solve linear inverse problems. Model-based methods incorporate certain assumptions, such as the image prior distribution, into an iterative estimation algorithm, often, as an example, solving a regularized least squares problem. Instead, data-driven methods learn the inverse reconstruction mapping directly by training a neural network structure on actual signal and signal measurement pairs. Alternatively, algorithm unrolling, a recent approach to inverse problems, combines model-based and data-driven methods through the implementation of an iterative estimation algorithm as a deep neural network (DNN). This approach offers a vehicle to embed domain-level and algorithmic insights into the design of neural networks such that the network layers are interpretable. The performance, in reconstructed signal quality, of unrolled DNNs often exceeds that of corresponding iterative algorithms and standard DNNs while doing so in a computationally efficient fashion. In this work, we leverage algorithm unrolling to combine a powerful statistical prior, the compound Gaussian (CG) prior, with the powerful representational ability of machine learning and DNN approaches. Specifically, first we construct a novel iterative CG-regularized least squares algorithm for signal reconstruction and provide a computational theory for this algorithm. Second, using algorithm unrolling, the newly developed CG-based least squares iterative algorithm is transformed into an original DNN in a manner to facilitate the learning of the optimization landscape geometry. Third, a generalization on the newly constructed CG regularized least squares iterative algorithm is developed, theoretically analyzed, and unrolled to yield a novel state-of-the-art DNN that provides a partial learning of the prior distribution constrained to the CG class of distributions. Fourth, techniques in statistical learning theory are employed for deriving original generalization error bounds on both unrolled DNNs to substantiate theoretical guarantees of each neural network when estimating signals from linear measurements after training. Finally, ample numerical experimentation is conducted for every new CG-based iterative and DNN approach proposed in this paper. Simulation results show our methods outperform previous state-of-the-art iterative signal estimation algorithms and deep-learning-based methods, especially with limited training datasets.Item Open Access Detection of linear algebra operations in polyhedral programs(Colorado State University. Libraries, 2016) Iooss, Guillaume, author; Rajopadhye, Sanjay, advisor; Alias, Christophe, advisor; Darte, Alain, advisor; Clauss, Philippe, committee member; Sankaranarayanan, Sriram, committee member; Thomassé, Stephan, committee member; Chitsaz, Hamid, committee member; Mueller, Jennifer, committee memberWriting a code which uses an architecture at its full capability has become an increasingly difficult problem over the last years. For some key operations, a dedicated accelerator or a finely tuned implementation exists and delivers the best performance. Thus, when compiling a code, identifying these operations and issuing calls to their high-performance implementation is attractive. In this dissertation, we focus on the problem of detection of these operations. We propose a framework which detects linear algebra subcomputations within a polyhedral program. The main idea of this framework is to partition the computation in order to isolate different subcomputations in a regular manner, then we consider each portion of the computation and try to recognize it as a combination of linear algebra operations. We perform the partitioning of the computation by using a program transformation called monoparametric tiling. This transformation partitions the computation into blocks, whose shape is some homothetic scaling of a fixed-size partitioning. We show that the tiled program remains polyhedral while allowing a limited amount of parametrization: a single size parameter. This is an improvement compared to the previous work on tiling, that forced us to choose between these two properties. Then, in order to recognize computations, we introduce a template recognition algorithm. This template recognition algorithm is built on a state-of-the-art program equivalence algorithm. We also propose several extensions in order to manage some semantic properties. Finally, we combine these two previous contributions into a framework which detects linear algebra subcomputations. A part of this framework is a library of template, based on the BLAS specification. We demonstrate our framework on several applications.Item Open Access Enacted responsiveness and responsiveness as a disposition: leveraging and valuing student thinking(Colorado State University. Libraries, 2019) Gehrtz, Jessica R., author; Hagman, Jess E., advisor; Byerley, Cameron, committee member; Mueller, Jennifer, committee member; Gloeckner, Gene, committee member; Speer, Natasha, committee memberOver the past few decades there has been increased attention on instructional practices that incorporate and build on student thinking. To effectively implement these practices, it is essential for an instructor to demonstrate responsiveness to student thinking. Although important, responsiveness is not well-understood at the post-secondary level. In this three-paper dissertation, I first use a thematic analysis to analyze twenty-nine articles that discuss constructs related to responsiveness to student thinking from within the K-16 science and mathematics education literature. Results from this analysis shed light on a distinction between responsiveness as a disposition and enacted responsiveness, which is articulated in the definition for responsiveness to student thinking that I propose. To better understand instructional practices that interact with and impact instructor responsiveness, in the second paper I analyze results from an instructional practices survey that was distributed to college calculus instructors at twelve institutions. Results from quantitative analyses highlight categorizations of instructional practice that relate to responsive practices, indicating that responsiveness can occur in both student-oriented and instructor-oriented classes. In the third paper, I investigate instructor responsiveness to student thinking as a disposition (that guides action) and responsiveness to student thinking as an action (the enacted evidence of the underlying disposition), drawing on interview data from eight college calculus instructors. A thematic analysis of the task-based interviews indicated that instructors who exhibited a responsive disposition to their students' thinking enact this through eliciting student thinking, reflecting on student thinking, and responding to student thinking. Further, these instructors view themselves as decision-makers, and thus feel empowered to act on their responsive disposition. The results from this dissertation have implications for researchers interested in teacher growth and professional development providers.Item Open Access Generalized full sparse tiling of loop chains(Colorado State University. Libraries, 2013) Krieger, Christopher D., author; Strout, Michelle Mills, advisor; Böhm, Wim, committee member; Rajopadhye, Sanjay, committee member; Mueller, Jennifer, committee memberComputer and computational scientists are tackling increasingly large and complex problems and are seeking ways of improving the performance of their codes. The key issue faced is how to reach an effective balance between parallelism and locality. In trying to reach this balance, a problem commonly encountered is that of ascertaining the data dependences. Approaches that rely on automatic extraction of data dependences are frequently stymied by complications such as interprocedural and alias analysis. Placing the dependence analysis burden upon the programmer creates a significant barrier to adoption. In this work, we present a new programming abstraction, the loop chain, that specifies a series of loops and the data they access. Given this abstraction, a compiler, inspector, or runtime optimizer can avoid the computationally expensive process of formally determining data dependences, yet still determine beneficial and legal data and iteration reorderings. One optimization method that has been previously applied to irregular scientific codes is full sparse tiling. Full sparse tiling has been used to improve the performance of a handful of scientific codes, but in each case the technique had to be applied from scratch by an expert after careful manual analysis of the possible data dependence patterns. The full sparse tiling approach was extended and generalized as part of this work to apply to any code represented by the loop chain abstraction. Using only the abstraction, the generalized algorithm can produce a new data and iteration ordering as well as a parallel execution schedule. Insight into tuning a generalized full sparse tiled application was gained through a study of the different factors influencing tile count. This work lays the foundation for an efficient autotuning approach to optimizing tile count.Item Open Access HIV-1 Gag trafficking and assembly: mathematical models and numerical simulations(Colorado State University. Libraries, 2013) Munoz-Alicea, Roberto, author; Liu, Jiangguo, advisor; Tavener, Simon, advisor; Chen, Chaoping, committee member; Mueller, Jennifer, committee member; Shipman, Patrick, committee memberAIDS (acquired immune deficiency syndrome) is an infectious disease that takes away many people's lives each year. Group-specific antigen (Gag) polyprotein precursor is the major structural component of HIV, the causing agent of AIDS. Gag is essential and sufficient for the formation of new HIV virus-like particles. The late stages of the HIV-1 life cycle include the transport of Gag proteins towards the cell membrane, the oligomerization of Gag near the cell membrane during the budding process, and core assembly during virion maturation. The mechanisms for Gag protein trafficking and assembly are not yet fully understood. In order to gain further insight into the mechanisms of HIV-1 replication, we develop and analyze mathematical models and numerical algorithms for intracellular Gag protein trafficking, Gag trimerization near the cell membrane, and HIV-1 core assembly. Our preliminary results indicate that active transport plays an important role for Gag trafficking in the cytoplasm. This process can be mathematically modeled by convection-diffusion equations, which can be solved efficiently using characteristic finite element methods. We employ differential dynamical systems to model Gag trimerization and HIV-1 core assembly. For the Gag trimerization model, we estimate relationships between the association and dissociation parameters as well as the Gag arrival and multimerization parameters. We also find expressions for the equilibrium concentrations of the monomer and trimer species, and show that the equilibrium is asymptotically stable. For HIV-1 core assembly, we first consider a model developed by Zlonick and others, which regards assembly as a polymerization reaction. We utilize theoretical and numerical tools to confirm the stability of the equilibrium of CA intermediates. In addition, we propose a cascaded dynamical system model for HIV-1 core assembly. The model consists of two subsystems: one subsystem for nucleation and one for elongation. We perform simulations on the nucleation model, which suggests the existence of an equilibrium of the CA species.Item Open Access Modeling local pattern formation on membrane surfaces using nonlocal interactions(Colorado State University. Libraries, 2015) Adkins, Melissa, author; Zhou, Yongcheng, advisor; Krapf, Diego, committee member; Liu, James, committee member; Mueller, Jennifer, committee memberThe cell membrane is of utmost importance in the transportation of nutrients and signals to the cell which are needed for survival. The magnitude of this is the inspiration for our study of the lipid bilayer which forms the cell membrane. It has been recently accepted that the lipid bilayer consists of lipid microdomains (lipid rafts), as opposed to freely moving lipids. We present two lipid raft models using the Ginzburg-Landau energy with addition of the electrostatic energy and the geodesic curvature energy to describe the local pattern formation of these lipid rafts. The development and implementation of a C⁰ interior penalty surface finite element method along with an implicit time iteration scheme will also be discussed as the optimal solution technique.Item Open Access Neural network security and optimization for single-person authentication using electroencephalogram data(Colorado State University. Libraries, 2022) Andre, Naomi, author; Simske, Steve, advisor; Mueller, Jennifer, committee member; Lyons, Michael, committee memberSecurity is an important focus for devices that use biometric data, and as such security around authentication needs to be considered. This is true for brain-computer interfaces (BCIs), which often use electroencephalogram (EEG) data as inputs and neural network classification to determine their function. EEG data can also serve as a form of biometric authentication, which would contribute to the security of these devices. Neural networks have also used a method known as ablation to improve their efficiency. In light of this info, the goal of this research is to determine whether neural network ablation can also be used as a method to improve security by reducing a network's learning capabilities to include authenticating only a given target, and preventing adversaries from training new data to be authenticated. Data on the change in entropy of weight values of the networks after training was also collected for the purpose of determining patterns in weight distribution. Results from a set of ablated networks to a set of baseline (non-ablated) networks for five targets chosen randomly from a data set of 12 people were compared. The results found that ablated maintained accuracy through the ablation process, but that they did not perform as well as the baseline networks. Change in performance between single-target authentication and target-plus-invader authentication was also examined, but no significant results were found. Furthermore, the change in entropy differed between both baseline networks and ablated networks, as well as between single-target authentication and target-plus-invader authentication for all networks. Ablation was determined to have potential for security applications that need to be expanded on, and weight distribution was found to have some correlation with the complexity of an input to a network.Item Open Access Nonlinear dynamics of plant pigmentation(Colorado State University. Libraries, 2022) Hsu, Wei-Yu, author; Shipman, Patrick, advisor; Mueller, Jennifer, committee member; Bradley, Richard, committee member; Finke, Richard, committee memberRed, blue, and purple colors in plants are primarily due to plant pigments called anthocyanins. In a plant cell, an equilibrium is established between anionic and cationic forms of anthocyanins as well electrically neutral colorless forms called hemiketals. In typical cellular pH ranges, the colorless hemiketal would be expected to be the dominant form. Why then, do plants, in fact, display colors? We propose that this is part due to self association and intermolecular association of the colored forms of anthocyanins. We develop a series of models for the interconversion of the colorless and colored forms of anthocyanins, including zwitterionic species and extend these models to include association of the colored species. Analysis of these models leads us to suggest and implement experiments in which the total concentration changes over time, either slowly or quickly compared to the kinetics. Coupling these models to a system of partial differential equations for in vivo anthocyanin synthesis (a modification of the Gierer-Meinhardt activator-inhibitor model), we simulate and analyze a variety of colorful spotted patterns in plant flowers. These studies are aided by a linear stability analysis and nonlinear analysis of the modified Gierer-Meinhardt model. The extended model that we propose is a first model to analyze the effects of association in pattern formation. Association may occur with various geometries which have an effect on the absorbance spectrum. Based on the Beer–Lambert law and our evaporative experiments, we develop methods of deconvoluting absorbance spectra of anthocyanin solutions into absorbance spectra of monomers, dimers and trimers, thus providing clues into the geometry of the smallest associated particles. Finally, we propose a novel geometric method of probing association by observing the changing shape of evaporating solution droplets. The associated mathematical model involves solving the highly nonlinear mean-curvature equation with nonconstant mean curvature (surface tension), and we present new solutions making use of the hodograph transform.Item Open Access Nucleation and growth: modeling the NH3 - HCL reaction(Colorado State University. Libraries, 2012) Shinn, Jaime M., author; Shipman, Patrick, advisor; Liu, James, committee member; Mueller, Jennifer, committee member; Thompson, Stephen, committee memberOne of the trademarks of a Liesegang ring system is the exhibition of a moving reaction front to form a periodic precipitation pattern. This phenomenon has been studied by both chemists and mathematicians. The periodic patterns produced have developed an interest from a mathematical perspective, while the theory and mechanism behind these patterns has created interest from a chemist's point of view. Many mathematical models have been proposed, and much interest has been invested in studying the mechanism behind these Liesegang ring systems. In particular, we will consider the NH3-HCl system, a gas-phase system in which the two gases (NH3 and HCl) diffuse into a tube and meet to form a solid precipitate. The reaction front then moves down the tube, forming a Liesegang banding pattern along the way. In this thesis, we derive a model for this system and examine some results of the model, which contribute to the theory and mechanism behind the NH3-HCl system. We predict the position of the first and last Liesegang band formed, and we examine the effect of the tube length of our system. Front velocity data from the model has also been obtained and is shown to correlate well with experimental data. We also note that the width of the heterogeneous nucleation zone increases as the concentration ratio of NH3 to HCl decreases, and we discuss the effect that water vapor has on the system.Item Open Access Resource allocation for space domain awareness and synthetic aperture radar(Colorado State University. Libraries, 2022) Owens-Fahrner, Naomi, author; Cheney, Margaret, advisor; Mueller, Jennifer, committee member; Shipman, Patrick, committee member; Chandrasekar, Venkatachalam, committee memberIn this thesis, we will address two resource allocation problems. For each of these problems, the objective will be to make use of the resources in an optimal way. We will consider the Space Domain Awareness (SDA) sensor tasking problem as well as the Synthetic Aperture Radar (SAR) flight path planning problem. We will first present a new objective function for the problem of Space Domain Awareness resource allocation (SDARA) as well as a novel algorithm to maximize this new objective function. This SDARA problem aims to maximize the total number of targets seen while minimizing resource costs. These resources, namely the optical sensors, are assumed to be heterogeneous and have different associated tasking costs. The novel algorithm, called the "block greedy" algorithm, provides an approximate regional maximum of this objective function in a tractable amount of time. The block greedy algorithm is a hybrid of the weapon-target-assignment and greedy algorithms. This algorithm will be shown to outperform common algorithms used in solving the SDARA problem. Second, we will present an approach to create an optimal SAR flight path by varying the vehicle's heading, pitch, and antenna steering angles. An optimal flight path is one in which the scene coverage and resolution are maximized. We will utilize the data-collection manifold as a tool to measure scene resolution. We will then add a scene coverage consideration to build an objective function in which we can plan an optimal flight path for an aircraft. After this, we will consider many extensions and applications of using this objective function. These include adding a signal-to-noise ratio (SNR) consideration to SAR flight path planning. Additionally, we will extend this objective function to include multiple unmanned aerial vehicle (UAVs) for optimal flight paths for a SAR system. We will use our objective function to optimally plan flight paths for multiple UAVs.Item Open Access Synthetic aperture source localization(Colorado State University. Libraries, 2018) Waddington, Chad, author; Cheney, Margaret, advisor; Pinaud, Oliver, committee member; Mueller, Jennifer, committee member; Given, James, committee member; Yang, Liuqing, committee memberThe detection and localization of sources of electromagnetic (EM) radiation has many applications in both civilian and defense communities. The goal of source localization is to identify the geographic position of an emitter of some radiation from measurements of the elds that the source produces. Although the problem has been studied intensively for many decades much work remains to be done. Many state-of-the-art methods require large numbers of sensors and perform poorly or require additional sensors when target emitters transmit highly correlated waveforms. Some methods also require a preprocessing step which attempts to identify regions of the data which come from emitters in the scene before processing the localization algorithm. Additionally, it has been proven that pure Angle of Arrival (AOA) techniques based on current methods are always suboptimal when multiple emitters are present. We present a new source localization technique which employs a cross correlation measure of the Time Dierence of Arrival (TDOA) for signals recorded at two separate platforms, at least one of which is in motion. This data is then backprojected through a Synthetic Aperture Radar (SAR)-like process to form an image of the locations of the emitters in a target scene. This method has the advantage of not requiring any a priori knowledge of the number of emitters in the scene. Nor does it rest on an ability to identify regions of the data which come from individual emitters, though if this capability is present it may improve image quality. Additionally we demonstrate that this method is capable of localizing emitters which transmit highly correlated waveforms, though complications arise when several such emitters are present in the scene. We discuss these complications and strategies to mitigate them. Finally we conclude with an overview of our method's performance for various levels of additive noise and lay out a path for advancing study of this new method through future work.Item Open Access Transient analysis of closed- and open-region electromagnetic problems using higher order finite element method and method of moments in the time domain(Colorado State University. Libraries, 2015) Šekeljić, Nada J., author; Notaroš, Branislav M., advisor; Mueller, Jennifer, committee member; Reising, Steven C., committee member; Chandrasekar, V., committee member; Ilić, Milan M., committee memberThe principal objective of this dissertation is to develop computational electromagnetic (CEM) methodology and tools for modeling of closed (waveguide and cavity based) and open (radiation and scattering) electromagnetic structures in the time domain (TD), employing two CEM approaches. The first method is a novel higher order and large-domain Galerkin finite element method (FEM) for transient analysis of multiport microwave waveguide devices with arbitrary metallic and dielectric discontinuities. It is based on geometrical modeling using Lagrange interpolation generalized hexahedral elements, spatial field expansion in terms of hierarchical curl-conforming polynomial vector basis functions, time-stepping with an implicit unconditionally stable finite difference scheme using the Newmark-beta method, and mesh truncation introducing the waveguide port boundary condition. The second method is a novel spatially large-domain and temporally entire-domain method of moments (MoM) proposed for surface integral equation (SIE) modeling of 3-D conducting scatterers in the TD. The method uses higher order curved Lagrange interpolation generalized quadrilateral geometrical elements, higher order spatial current expansions based on hierarchical divergence-conforming polynomial vector basis functions, and temporal current modeling by means of orthogonal weighted associated Laguerre basis functions. It implements full temporal and spatial Galerkin testing and marching-on-in-degree (MOD) scheme for an iterative solution of the final system of spatially and temporally discretized MoM-TD equations. Numerical examples of waveguides and scatterers, modeled using flat and curved large elements in conjunction with field/current expansions of orders from 2 to 9, demonstrate excellent accuracy, efficiency, convergence, and versatility of the proposed methodologies. The results obtained by higher order TD-FEM and TD-MoM are in an excellent agreement with indirect solutions obtained from FEM and MoM analyses in the frequency domain (FD) in conjunction with discrete Fourier transform and its inverse, as well as with measurements and alternative full-wave numerical solutions in both TD and FD.